caa a22 4500 463177223 CHVBK 20180406164829.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10986-007-0015-9 doi (NATIONALLICENCE)springer-10.1007/s10986-007-0015-9 Stupelis L. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania aut On solvability of an initial-boundary-value problem for equations of magnetohydrodynamics [Elektronische Daten] [L. Stupelis] In this paper, we consider a nonstationary problem of magnetohydrodynamics (MHD) for viscous incompressible fluid under the condition that the medium is poorly conducting. The problem is analyzed in a bounded one-connected domain Ω ⊂ ℝn, n = 2,3, for t > 0 under the condition of ideal conductivity on the boundary. We prove a theorem on the unique solvability of the problem "in the small,” on a small time interval, and on a given time interval ]0, T[ (including T = +∞) when the given data of the problem are sufficiently small (precise formulations are given in Sect. 2). To investigate the nonlinear problem, several auxiliary linear problems are preliminarily considered. The results of this paper were announced by the author in the Trakai Conference on Mathematical Modeling and Analysis in spring of 2005. Springer Science+Business Media, Inc., 2007 Navier-Stokes nationallicence incompressible fluid nationallicence L q -theory nationallicence Maxwell nationallicence dissipative hyperbolic systems nationallicence magnetohydrodynamics nationallicence displacement currents nationallicence electrodynamic radiation nationallicence electrodynamics nationallicence Lithuanian Mathematical Journal Springer US 47/2(2007-04-01), 195-227 0363-1672 47:2<195 2007 47 10986 https://doi.org/10.1007/s10986-007-0015-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10986-007-0015-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Stupelis L. Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania aut NATIONALLICENCE 773 0- Lithuanian Mathematical Journal Springer US 47/2(2007-04-01), 195-227 0363-1672 47:2<195 2007 47 10986 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer